Digital Camera with Apparatus for Authentication of Images Produced from an Image File

A digital camera equipped with a processor for authentication of images produced from an image file taken by the digital camera is provided. The digital camera processor has embedded therein a private key unique to it, and the camera housing has a public key that is so uniquely related to the private key that digital data encrypted with the private key may be decrypted using the public key. The digital camera processor comprises means for calculating a hash of the image file using a predetermined algorithm, and second means for encrypting the image hash with the private key, thereby producing a digital signature. The image file and the digital signature are stored in suitable recording means so they will be available together. Apparatus for authenticating the image file as being free of any alteration uses the public key for decrypting the digital signature, thereby deriving a secure image hash identical to the image hash produced by the digital camera and used to produce the digital signature. The authenticating apparatus calculates from the image file an image hash using the same algorithm as before. By comparing this last image hash with the secure image hash, authenticity of the image file is determined if they match. Other techniques to address time-honored methods of deception, such as attaching false captions or inducing forced perspectives, are included

Polylog Depth Circuits for Integer Factoring and Discrete Logarithms

AbstractIn this paper, we develop parallel algorithms for integer factoring and for computing discrete logarithms. In particular, we give polylog depth probabilistic boolean circuits of subexponential size for both of these problems, thereby solving an open problem of Adleman and Kompella. Existing sequential algorithms for integer factoring and discrete logarithms use a prime base which is the set of all primes up to a bound B. We use a much smaller value for B for our parallel algorithms than is typical for sequential algorithms. In particular, for inputs of length n, by setting B = nlogdn with d a positive constant, we construct •Probabilistic boolean circuits of depth (log) and size exp[(/log)] for completely factoring a positive integer with probability 1−(1), and •Probabilistic boolean circuits of depth (log + log) and size exp[(/log)] for computing discrete logarithms in the finite field () for a prime with probability 1−(1). These are the first results of this type for both problem

On the computation of discrete logarithms in finite prime fields

In this thesis we write about practical experience when solving congruences of the form a^x = b mod p, a,b,p,x Element Z, p prime. This is referred to as the discrete logarithm problem in (Z/pZ)*. Many cryptographic protocols such as signature schemes, message encryption, key exchange and identification depend on the difficulty of this problem. We are concerned with the practicability of different index calculus variants, which are the asymtotically fastest known algorithms at present to solve this problem. We present computations for p having up to 85 decimal digits. We include a partial solution to McCurley\u27s challenge with a 129-digit p, which has a special form.In dieser Arbeit berichten wir über praktische Erfahrungen mit der Lösung von Kongruenzen der Form a^x = b mod p, a,b,p,x Element Z, p Primzahl. Dies ist das Problem der Diskreten Logarithmen in (Z/pZ)*. Zahlreiche kryptographische Protokolle wie digitale Unterschriften, Verschlüsselung von Nachrichten, Schlüsselaustausch und Identifikation basieren auf der Schwierigkeit dieses Problems. In dieser Arbeit befassen wir uns mit der Praktikabilität verschiedener Index-Calculus Verfahren, die zur Zeit die asymptotisch schnellsten Algorithmen liefern, um dieses Problem zu lösen. Wir präsentieren Berechnungen mit bis zu 85-stelligem p und legen eine partielle Lösung zu McCurley\u27s Challenge vor, die ein 129-stelliges p von spezieller Form benutzt